text: Let  and  be the velocity, pressure and strain rate tensor of the Stokes flow and  and  be the velocity, pressure and strain rate tensor of any other incompressible motion with  on the boundary. Let  and  be the representation of velocity and strain tensor in index notation, where the index runs from one to three.
  Consider the following integral,
  where in the above integral, only symmetrical part of the deformation tensor remains, because the contraction of symmetrical and antisymmetrical tensor is identically zero. Integration by parts gives 
  The first integral is zero because velocity at the boundaries of the two fields are equal. Now, for the second integral, since  satisfies the Stokes flow equation, i.e., , we can write
  Again doing an Integration by parts gives
  The first integral is zero because velocities are equal and the second integral is zero because the flow in incompressible, i.e., . Therefore we have the identity which says,
  The total rate of viscous dissipation energy over the whole volume of the field  is given by
  and after a rearrangement using above identity, we get
  If  is the total rate of viscous dissipation energy over the whole volume of the field , then we have
  The second integral is non-negative and zero only if , thus proving the theorem.